SOLVING EQUATIONS WITH ABSOLUTE VALUES ON BOTH SIDES

The picture shown below explains how to solve the equations in which we have absolute value sign on both sides.

Example 1 :

Solve for x :

|x - 3| = |3x + 2|

Solution :

Based on the idea given above, we have

Justify and evaluation :

Substitute x = -5/2 and x = 1/4 in the given absolute value equation. 

Substituting x = -5/2 and x = 1/4 into the original equation results in true statements.

Both the answers x = -5/2 and x = 1/4 are correct and acceptable.

Problem 2 :

Solve for x :

|x - 7| = |2x - 2|

Solution :

Based on the idea given above, we have

Justify and evaluation :

Substitute x = -5 and x = 3 in the given absolute value equation.

Substituting x = -5 and x = 3 into the original equation results in true statements.

Both the answers x = -5 and x = 3 are correct and acceptable.

Problem 3 :

Solve for z :

|2z + 5| = |2z - 1|

Solution :

Based on the idea given above, we have

Justify and evaluation :

Substitute z = -1 in the given absolute value equation.

|2(-1) + 5| = |2(-1) - 1|

|-2 + 5| = |-2 - 1|

|3| = |-3|

3 = 3

Substituting z = -1 into the original equation results in true statement. 

So, the answer z  = -1 is correct and acceptable.

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